The invention relates to general electromagnetic simulation and electromagnetic field data processing for signal integrity analysis. More particularly, the invention relates to a method and computer system for solving complicated electromagnetic simulation problems in high-speed integrated circuit (IC) signal integrity analysis.
During electrical analyses of devices that are small with respect to wavelength, such as electronic packaging structures, chips, interconnects, and printed circuit boards, linear systems of equations must be solved. The present invention enhances existing electromagnetic simulation EDA tools using a novel Huygens' box methodology. The novel method and system requires use of only electric field integral equations (EFIE) instead of both EFIE and magnetic field integral equations (MFIE).
A Huygens' box approach to electromagnetic analysis of electronic structures includes constructing a large structure or domain from a set of smaller, non-overlapping sub-domains. The field property of the internal sub-domains are replaced with equivalent sources on the outer surfaces, i.e., discretized point sources. Each sub-domain is analyzed separately, without regard to the others. The method may be used enable conventional EDA tools to analyze complicated structures by compartmentalizing the problem into smaller equivalent units with fewer unknowns. As such, the present invention may serve as an industry standard to organize outputs from different electromagnetic vendor tools, generate parameterized model library databases, and in a readily parallelizable process.
A nested equivalence principle algorithm (NEPAL) that divides scattering objects into subgroups is known. W. C. Chew and C. C. Lu, “NEPAL—An Algorithm for Solving the Volume Integral Equation,” Microwave and Optical Technology Letters, vol. 6, no. 3, pp 185-188, Mar. 5, 1993 (“Chew and Lu (1)”). For each subgroup, the NEPAL algorithm substitutes interior scatterers with boundary sub-scatterers using Huygens' equivalence principle. The subgroups are combined by levels to achieve a computational complexity of O(N2) for non-iterative solutions to 3D scattering problems. The NEPAL Algorithm, however, uses spherical point sources as the equivalent sources so that solving electromagnetic scattering of 3D objects using spherical wave manipulation is very complicated. W. C. Chew and C. C. Lu, “The Use of Huygens' Equivalence Principle for Solving the Volume Integral Equation of Scattering,” IEEE Trans. Antennas and Propagat., vol. 41, no. 7, pp. 897-904, July 1993 (“Chew and Lu (2)”); and C. C. Lu and W. C. Chew, “The Use of Huygens' Equivalence Principle for Solving 3-D Volume Integral Equation of Scattering,” IEEE Trans. Antennas and Propagat., vol. 43, no. 5, pp. 500-507, May 1995 (“Lu and Chew (3)”).
Known alternative techniques include the use of a combination of surface integral equations, and apply a form of Huygens' equivalence principle. M.K. Li and W.C. Chew, “Wave-Field Interaction with Complex Structures Using Equivalence Principle Algorithm,” UIUC CCEM Lab Research Report, 2006 (“Li and Chew (4)”), and M. K. Li, W. C. Chew and L.J. Jiang, “A Domain Decomposition Scheme to Solve Integral Equations Using Equivalent Surfaces,” 2006 IEEE Antennas and Propagation Society International Symposium, pp. 2897-2900, Albuquerque, N.M., USA (“Li and Chew (5).”). These alternative techniques use both electric field and magnetic field to build the field response for an enclosed sub region to mimic the general [S] parameters. Boundary equivalent sources based on surface basis are used to preserve the sub region interactions. A nesting process similar to NEPAL is employed to combine sub regions. Since both EFIE (Electric Field Integral Equation) and MFIE (Magnetic Field Integral Equation) are involved, however, many operators are needed, rendering such an implementation process complicated.
Also known is a reduced-coupling method implemented to deduce the dense interactions through boundary ports. B. J. Rubin, A. Mechentel, and J. H. Magerlein, “Electrical Modeling of Extremely Large Packages,” 1997 Electronic Components and Technology Conference, pp 804-809 (“Rubin (6)”); and US Pending Application Serial No. 2005/0222825 to Feldmann, et al., Method, Apparatus and Computer Program Providing Broadband Preconditioning Based on Reduced Coupling For Numerical Solvers (“the '825 application”). Rubin (6) and the '825 application accelerate the computational process, but not rigorously since the connecting boundaries are not closed.